Backinterpolation Methods for the Numerical Solution
of Ordinary Differential Equations and Applications
Abstract
This thesis presents backinterpolation (BI) methods for the numerical solution
of ordinary differential equations (ODE) and their applications. Compared with
conventional numerical integration algorithms, BI methods are more effective
in handling marginally stable and stiff problems. Stability properties of BI
methods have been investigated, and a method for calculating their stability
domains has been developed. Issues related to accuracy considerations of BI
algorithms have been addressed. Procedures for constructing accuracy domains
for BI methods have been given. A study of damping and frequency properties of
these methods has been conducted. Programs for comparing analytical and
discrete damping and frequency along an arbitrary axis have been specified.
A scheme of stepsize control for BI methods has been proposed. Two algorithms
of adjusting stepsizes have been evaluated through simulations.
To demonstrate the effectiveness and efficiency of BI methods in solving
marginally stable and stiff problems, ODE models for dynamic responses of
one-link flexible manipulators have been developed and solved using
BI methods. For both open-loop (marginally stable) and closed-loop (stiff)
configurations, numerical results have demonstrated the effectiveness of BI
methods for solving these types of problems.
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Last modified: July 20, 2005 -- © François Cellier